How do I solve: how to solve 3x=4(4-2x)=11 and
x-2y+4z=9
x=2z+2
y=-4z ?
Thanks Need ASAP
3x=4(4-2x)=11
I suspect a typo
yes its supposed to be 3x+4(4-2x)=11
To solve the equations 3x=4(4-2x)=11 and x-2y+4z=9, x=2z+2, and y=-4z, we need to apply some algebraic techniques.
First, let's break down the equations one by one:
Equation 1: 3x=4(4-2x)=11
There seems to be an error in this equation. It is written with two equal signs (=), which is not correct. To proceed, we need to determine the correct equation.
Equation 2: x - 2y + 4z = 9
Equation 3: x = 2z + 2
Equation 4: y = -4z
Now, let's solve the system of equations by substituting variables using Equations 3 and 4 into Equation 2:
Substituting Equation 3 into Equation 2:
(2z + 2) - 2y + 4z = 9
Simplifying:
2z + 2 - 2y + 4z = 9
6z - 2y + 2 = 9
Rearranging the equation:
6z - 2y = 7
Next, substitute Equation 4 into the new Equation:
6z - 2(-4z) = 7
6z + 8z = 7
14z = 7
z = 7/14
z = 1/2
Now that we have the value of z, we can substitute it into Equation 3 to find the value of x:
x = 2(1/2) + 2
x = 1 + 2
x = 3
Finally, we can substitute the values of x and z back into Equation 4 to find the value of y:
y = -4(1/2)
y = -2
So the solutions for the given system of equations are x = 3, y = -2, z = 1/2.
Please double-check the original equation (Equation 1) for any errors, as it appears to have been written incorrectly.